Contents:

Part I. Modelling Framework 1 1. The Black-Scholes Framework 3 1.1 The Black-Scholes equity model 3 1.2 Extentions to Black-Scholes 6 2. Skew Models 13 2.1 Introduction 13 2.2 Volatility surface generation 15 2.3 Volatility smile model 18 2.4 Volatility surface dynamics 20 3. Jump-Diffusion Models 23 3.1 Model Description 23 3.2 Options pricing 25 3.3 Fitting the smile 27 4. Deterministic Volatility Models 31 4.1 Introduction 31 4.2 Calibration techniques 33 4.3 Hedging 36 5. Stochastic Volatility Models 39 5.1 The Hull-White model 39 5.2 The Heston Model 41 5.3 Calibration 43 5.4 Hedging 45 5.5 Introduction to Arch and Garch 46 6. Credit Spread Models 51 6.1 Merton's model 52 6.2 Structural models 53 6.3 Intensity models 53 6.4 Convertible bonds with credit risk 57 Part II. Numerical Techniques 63 7. Trees 65 7.1 Thich tree 65 7.2 Implied trees 66 7.3 Stochastic trees 69 7.4 Generic tree framework 74 8. Finite Difference 77 8.1 One-dimensional techniques 77 8.2 Path-dependant options 83 8.3 Two-dimensional techniques 85 8.4 Generic finite difference 87 9. Monte Carlo 89 9.1 Local volatility in Monte Carlo 89 9.2 Itô-Taylor expansion 90 9.3 Greeks in Monte Carlo 94 9.4 Generic Monte Carlo framework 102 10. Alternative Approaches 105 10.1 Fourier transforms 105 10.2 Laplace transforms 108 10.3 Path integral 109 Part III. Market Products 111 11. American Options on Multi Assets 113 11.1 Markov chain method 113 11.2 Regression for continuation method 115 11.3 Simulated tree 116 11.4 Stochastic mesh 117 12. Volatility Contracts 119 12.1 Variance swaps 120 12.2 Covariance swaps 124 12.3 Volatility swaps 126 12.4 Volaility options 134 13. Discrete Sampling Options 137 13.1 Barriers 137 13.2 Lookbacks 138 14. Additional Products 143 14.1 Cliquet with smile - analytical approximation 143 14.2 Barrier options with a smile 144 14.3 Passport options 146 Part IV. Risk Management 149 15. Introduction to Risk Management 151 15.2 Credit Risk 152 15.3 Raroc 153 16. Value-at-Risk 157 16.1 The VaR approach 158 16.2 VaR methodologies 164 16.3 Simulated VaR 164 16.4 Analytical VaR 169 16.5 Correlation concepts 174 17. Extreme Value Theory 177 17.1 The domain of attraction 177 17.2 A central limit theorem for maxima 179 17.3 Point process approach 182 17.4 Estimation of the tail distribution 183 17.5 A limit theorem for the excess distribution 186 17.6 The peaks over threshold (POT) method 188 17.7 Dynamic extreme value theory 190 17.8 Multi-day returns 194 17.9 Multivariate EVT 194 17.10 Hill estimation 195 18. Coherent Risk Measures 197 18.1 Axioms for acceptance sets 197 18.2 Correspondence between acceptance sets 198 and risk measures 18.3 Axioms for risk measures 198 18.4 Correspondence between the axioms on 198 acceptance sets and risk measures 18.5 Value-at-risk and expected shortfall 199 18.6 Model-free risk measures 200 18.7 Generalised senarios 201 19. Credit Risk Management 203 19.1 The asset value model 203 19.2 The credit quality migration model 207 19.2 Credit Risk+ 211 Bibliography 219